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We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under consideration include the kinetic Cucker--Smale equation Cucker and Smale, IEEE Trans. Automat. Control, 52 (2007), pp. 852--862, Cucker and Smale, Japan. J. Math., 2 (2007), pp. 197--227 with possibly nonsymmetric flocking potential, the Cucker--Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor J. Statist. Phys., 141 (2011), pp. 923--947. The main tools employed in the analysis are the velocity-averaging lemma and the Schauder fixed-point theorem along with various integral bounds.
Karper et al. (Tue,) studied this question.